The bedside phone in 6 Columbus, my New York hotel, rang twice. Then a familiar voice said: "You're seeing Don today. I'll join you for lunch afterwards." And that was how my interview with Don DeLillo began.

Looking back, I see that there could hardly be a more appropriate introduction to first meeting a writer who revels in bizarre irruptions of the unexpected into the even flow of time, unlikely juxtapositions of reality and strange collisions of character and personality.

In hindsight, too, this early-morning phone call did something else. It made the encounter with DeLillo, a giant of the contemporary American literary landscape, seem almost normal, intriguing and unintimidating. That's quite something: DeLillo is said, in virtually every interview I'd read about him, to resent the intrusions of journalists. He describes his relationship to his readers as "silence, exile, cunning, and so on", and used to carry a card that read simply: "I do not want to talk about it."

So today would be different. This would be "seeing Don" and afterwards we would have lunch with our mutual friend, Paul Auster. None the less, as I waited for our mid-morning appointment, I anxiously reviewed DeLillo's literary career once more, just in case.

DeLillo has devoted his writing to the shadow side of American life, painting a dysfunctional freaks' gallery of the wrecked (David Bell in Americana), the sick (Bill Gray in Mao II), the mad (Lee Harvey Oswald in Libra) and the suicidal (Eric Packer in Cosmopolis). In White Noise, the protagonist, Jack, who teaches Hitler studies, riffs hilariously on death and mass murder. It is said that DeLillo used to keep two files on his writing table, labelled "Art" and "Terror". In Mao II, he writes: "I used to think it was possible for an artist to alter the inner life of the culture. Now bomb-makers and gunmen have taken that territory." On some readings, his characters occupy this no-man's-land. His vision has been described as "paranoid" in the sense that it connects everything about his society.

In the process of exploring America, DeLillo has become credited with extraordinary powers of literary clairvoyance. The war on terror is said to be foreshadowed in Mao II. The planes that flew into the Twin Towers are possibly alluded to on the cover of Underworld. Parts of White Noise are echoed in the anthrax scare of 2001, and so on.

Fellow writers talk with admiration of DeLillo's creative radar. The truth is that DeLillo is wired into contemporary America from the ground up, spookily attuned to the weird vibrations of popular culture and the buzz of everyday, ordinary conversations on bus and subway. According to Joyce Carol Oates, he is "a man of frightening perception", an all-American writer who sees and hears his country like no other.

DeLillo's masterpiece, Underworld (1997), a portrait of cold-war America, declares its democratic, artistic agenda from its opening line: "He speaks in your voice, American, and there's a shine in his eyes that's halfway hopeful." Reviewers who had been watching DeLillo's work in the 80s and 90s, without becoming fully converted, now lined up to throw their hats in the air with a chorus of acclaim, a "home run", a "colossus", a "bible", a "wolf whistle" etc. Writing in the Observer, William Boyd commented: "In Underworld, we have a mature and hugely accomplished novelist firing on all cylinders... reading the book is a charged and thrilling aesthetic experience and one remembers gratefully that this is what the novel can do."

After Underworld, an 800-page tour de force, DeLillo's career turned towards the miniature: The Body Artist (2001), Cosmopolis (2003), The Falling Man (2007) are much slighter books, a rallentando that suggests a writer moving inexorably into the minor key of old age. Not that you'd find this in the demeanour of DeLillo.

When he hurries into the hotel foyer out of some atrocious weather, DeLillo is a slight, anonymous figure in a black cap and leather jacket who, once he has got past the initial introductions, seems to delight in the narrative possibilities of Auster's phone call. "If it was a story," he says in his distinctive Bronx twang, with a sly look for my reaction, "it would be called '6 Columbus'." DeLillo can be a dazzling writer, especially in his early books, but to meet he is quiet, guarded and thoughtful. Not flashy.

So how, I wonder, getting down to it, does he usually go about collecting the materials for his fiction? "I'm always keeping random notes on scraps of paper," he replies. "I always carry a pencil and a notebook. Coming on the train today I had an idea for a story I'm writing and jotted it down – on just a little scrap of paper. Then I clip these together. I'll look at them in, say, three weeks' time, and see what I've got. You know," he adds defiantly, "I've never made an outline for any novel that I've written. Never."

This is something of an artistic credo. DeLillo is at pains to suggest he is in no hurry with his work. The material must come to him. When it comes, he believes that "it has its own mandate", and cannot, he says, be wrenched into a narrative at odds with its deepest meaning. Yet behind the unflustered calm of the artist, there's the older man's consciousness of age. DeLillo is now in his early 70s. In his most recent book, Point Omega, there are references to "time" on almost every page. Perhaps art and life are finally approaching harmony. In a recent New York Review of Books, John Banville described DeLillo as "the poet of entropy. The world he sets up is a tightly wound machine gradually running down".

More of a novella, or a long short story, Point Omega is a fragment of classic DeLillo, apparently rooted in time and place: 2006, late summer, early fall. This was when DeLillo went to New York's Museum of Modern Art (Moma) to see Douglas Gordon's installation 24 Hour Psycho, a video work that slows down every frame of Hitchcock's thriller into a 24-hour cycle. Immediately, it hooked the writer's imagination. "Time and death," he remarks with some satisfaction. "It's the ultimate vision of an artist at the end of everything. It's just what's there. It was not something I planned to do."

In an oblique, attenuated way, Point Omega is DeLillo's response to the Iraq war. "Because of 9/11," he summarises, "Americans were in a mood to have faith in their government and they were angry. It was a huge mistake to attack." Was it a crime? He won't go there. "Rendition would qualify as a crime," he says carefully. This new book, he adds pointedly, is "about time and loss".

"I walked into the museum," he says, "and there was this video about which I knew virtually nothing. But I found it oddly compelling. You were looking at a screen on which practically nothing happens. And as I looked I saw that there was something in here about time and mortality. I went back two or three times. I thought: maybe this would inspire a work of fiction."

This is how DeLillo works. Despite having nothing in mind when he encountered 24 Hour Psycho, he let his imagination get to work, freely. "I had no idea what would happen and absolutely no idea what would happen later on in the novel." Readers who want neat plots and tidy endings should leave now. This is not DeLillo's concern. As he writes in his first chapter, in words for which he will disclaim responsibility: "The true life is not reducible to words spoken or written, not by anyone, ever."

Actually, in the use of Gordon's installation, there is an unconscious pattern. DeLillo likes to riff on contemporary art. There's the eponymous hero in The Body Artist. In Cosmopolis, he places a crowd of naked bodies in a street a la Spencer Tunick. Point Omega is what he calls "a triptych" whose prologue and unresolved epilogue take place in Moma.

Here, the mood is Beckett, out of the noir thrillers from DeLillo's Bronx childhood. A man and a woman, strangers, stand in front of the video installation in which time has run almost to a standstill. "I want to die after a long traditional illness," says the woman. "What about you?" After a bit, the man says: "Can you imagine yourself living another life?" To which the woman replies: "That's too easy. Ask me something else."

Face to face, DeLillo talks like a man who could imagine many lives and who has certainly run the gamut of the American dream. Confronted with a lifetime of experience, he confesses that his age "doesn't seem quite real. It's not meaningful. I can't quite imagine myself being 73. That's the age my father was!" He laughs. "How can I be his age? It's weird." So how old does he feel? "Well, I'm still in my 20s for sure. I'm pretty fit. I used to go for a daily run, but now I exercise at home to avoid the weather. I stick to a routine. But when I'm between work, I don't panic. I suppose I have the Italian element of enjoying a certain amount of leisure."

An all-American writer whose first novel was published, after a long struggle, as long ago as 1971, DeLillo's life is shaped in so many ways by his Italian-American roots and his need to fulfil his parents' ambition to assimilate the culture of the USA. "My parents [who were from Abruzzi] wanted American kids," he says, "and my sister and I had no motive in speaking Italian, though my parents were bilingual. My grandfather was a carpenter and my father eventually got a job that required him to wear a suit and tie, which was very important to him."

His father, who worked as a clerk in the Metropolitan Life Insurance Company, bought into the American dream and so, after a certain amount of goofing around, did the young DeLillo. "In a strange kind of way," he goes on, "what I did was to repeat the journey of my parents. That's to say, they left the old country to find a better life. When I started to write short stories in my early 20s they were set in the Italian Bronx. That's what I knew."

He was, he says, "a provincial kid who went to the local college". This was Fordham, a Jesuit school in the Bronx. "I wasn't qualified to go to an Ivy-League school. I was the only guy in America who walked to college." Inevitably, he lost whatever faith he had, studied religion and philosophy and, failing a medical, missed the draft. "Too young for Korea," he observes, "too old for Vietnam." At first, he went into advertising, as a copywriter with Ogilvy & Mather, fulfilling his parents' ambitions for their son.

DeLillo pauses in reflection. "But then it came time for me to make my journey – into America." It was, he says, "no coincidence that my first novel is called Americana. That became my subject, the subject that shaped my work. When I get a French translation of one of my books that says 'translated from the American', I think, 'Yes, that's exactly right.'"

There are many other subtle transactions at play in DeLillo's fiction. "When I work," he goes on, "I'm just translating the world around me in what seems to be straightforward terms. For my readers, this is sometimes a vision that's not familiar. But I'm not trying to manipulate reality. This is just what I see and hear."

He still considers himself as something of an outsider in his society and relishes the perspective his age gives his writing. The 1950s Bronx chapter in Underworld was, he says "a pleasure to write, exploring all those memories". Growing up as an Italian-American kid on the streets of the Bronx, he concedes that he was "remote from the wider world around me".

One of the first books that opened his adolescent eyes to the American scene was literary baseball fan James T Farrell's Studs Lonigan trilogy, set in Chicago, but evocative of the big-city life he was living. "That was a revelation," he says and a call to arms for a young man apprehensive about the next move. "Making the journey from the Bronx to Manhattan was a major undertaking."

DeLillo now lives in Westchester County in New York State with his wife, Barbara, a landscape designer, but he has not completely left his childhood neighbourhood, a place he insists still "looks the same, though the people are different": an influx of new immigrants, Serbs, Croats and African-Caribbeans. Every year, he goes back to meet old school friends from the streets of his childhood. "We meet on a major street and have a meal together and a laugh," he says. Inevitably, the conversation will turn to baseball, DeLillo's first love – what he calls his "second language". Baseball, he says, "was just so natural, because we all grew up with it. We played it; we listened to it on the radio, and then we went to Yankee stadium. It was a taken-for-granted pleasure".

DeLillo still had to make his journey "into America" and that was hard. "It took a long time," he says. "I was very slow to begin. I lacked the discipline for the enormous commitment one has to make. Even when I had all day to write, and sometimes all week, I took forever finally to enter my first novel." That was Americana, published in 1971 when he was 35.

"It was only after two years' work," he confesses, "that it occurred to me that I was a writer. I had no particular expectation that the novel would ever be published, because it was sort of a mess. It was only when I found myself writing things I didn't realise I knew that I said, 'I'm a writer now.' The novel had become an incentive to deeper thinking. That's really what writing is – an intense form of thought."

DeLillo likes to keep this intensity to himself, which has given him the label "reclusive". But he resists this. "I'm not reclusive at all. Just private." As a celebrated writer, and a shy man, he wants to keep it this way, with his fans held at arm's length. "This is the age of consumer fiction. People want fiction that's easily assimilable." That holds no interest for DeLillo. "Point Omega challenged me in the writing and I assume it will challenge some readers as well."

He relishes complexity and goes into a long account of Teilhard de Chardin's work and the idea of the "omega point", concluding, after an explanation of the "noosphere", with a note of triumph, that "these are not easy ideas to understand, but that's what we are dealing with". For DeLillo, the mystery of the process is a vital ingredient in fiction. "We are bound to wonder: where does this material come from?"

As a champion of "difficulty", albeit in an American mode, he is an heir of modernism and says that he sees himself as "part of a long modernist line starting with James Joyce". Unlike his friend Paul Auster, there's no part of his creative make-up that owes much to the 19th-century American masters. "I was too much of a Bronx kid to read Emerson or Hawthorne." Instead, he listens to jazz: "Charlie Mingus, Miles Davis, the same music I listened to when I was 20."

This comes as a reminder that DeLillo stands in the middle of a postwar generation of American writers, ranging from the senior (Philip Roth) to the junior (Paul Auster), all of them from the suburbs. "We are not native," DeLillo explains. "We have no generations of Americans behind us. We have roots elsewhere. We are looking in from the outside. To me, that seems to be perfectly natural."

As an outsider, DeLillo hates the publicity that comes with each new novel. For Point Omega,he made one public appearance, in Brooklyn, and observes with a laugh: "Everyone who does not live in Berlin lives in Brooklyn now." Does he like to read? "In public? No." I suggest that he prefers to keep his achievements to himself, even from his family. A smile: "My mother used to say, 'Who was gonna tell me?' She would see my picture in the newspaper and exclaim, 'Who was gonna tell me that a son of mine from Arthur Avenue in the Bronx was going to end up in the New York Times?' There was always a sense of wonder and unreality," he concludes. Is that the American dream? Another thin smile: "In a curious way, yes."

"What's next?" I ask. DeLillo shrugs. "Just a story." He gives a weak smile. "I don't know what's next." Is he happy with that? Another shrug. "I'm fine." A beat. "It's my contention that each book creates its own structure and its own length. I've written three or four slim books. It may be that the next novel is a big one, but I don't know."

We're done. Beyond the hotel foyer, we can see Paul Auster in his black leather jacket fighting his way through the weather for our lunchtime rendezvous. He and DeLillo decide we should go to the Carnegie Deli, an old-style New York hang-out on Seventh Avenue. In the expectation of traditional fare, the conversation morphs into a discussion about the difficulty of finding typewriter ribbons. Neither Auster nor DeLillo, who both habitually carry pencils and notebooks, uses word processors. This is where American literature begins.